Solve 92412-1r^220

Question

Simplify the expression

92412 - 20 r^{2}

Evaluate

92412 - 1 \times r^{2} \times 20

Solution

More Steps

Evaluate

1 \times r^{2} \times 20

Rewrite the expression

r^{2} \times 20

Use the commutative property to reorder the terms

20 r^{2}

92412 - 20 r^{2}

Show Solution

Factor the expression

4 (23103 - 5 r^{2})

Evaluate

92412 - 1 \times r^{2} \times 20

Multiply the terms

More Steps

Evaluate

1 \times r^{2} \times 20

Rewrite the expression

r^{2} \times 20

Use the commutative property to reorder the terms

20 r^{2}

92412 - 20 r^{2}

Solution

4 (23103 - 5 r^{2})

Show Solution

Find the roots

r_{1} = - \frac{3 12835}{5}, r_{2} = \frac{3 12835}{5}

Alternative Form

r_{1} \approx - 67.974995, r_{2} \approx 67.974995

Evaluate

92412 - 1 \times r^{2} \times 20

To find the roots of the expression,set the expression equal to 0

92412 - 1 \times r^{2} \times 20 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times r^{2} \times 20

Rewrite the expression

r^{2} \times 20

Use the commutative property to reorder the terms

20 r^{2}

92412 - 20 r^{2} = 0

Move the constant to the right-hand side and change its sign

- 20 r^{2} = 0 - 92412

Removing 0 doesn't change the value,so remove it from the expression

- 20 r^{2} = - 92412

Change the signs on both sides of the equation

20 r^{2} = 92412

Divide both sides

\frac{20 r ^{2}}{20} = \frac{92412}{20}

Divide the numbers

r^{2} = \frac{92412}{20}

Cancel out the common factor 4

r^{2} = \frac{23103}{5}

Take the root of both sides of the equation and remember to use both positive and negative roots

r = \pm \frac{23103}{5}

Simplify the expression

More Steps

Evaluate

\frac{23103}{5}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{23103}{5}

Simplify the radical expression

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Evaluate

23103

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 2567

Write the number in exponential form with the base of 3

3^{2} \times 2567

The root of a product is equal to the product of the roots of each factor

3^{2} \times 2567

Reduce the index of the radical and exponent with 2

32567

\frac{3 2567}{5}

Multiply by the Conjugate

\frac{3 2567 \times 5}{5 \times 5}

Multiply the numbers

More Steps

Evaluate

2567 \times 5

The product of roots with the same index is equal to the root of the product

2567 \times 5

Calculate the product

12835

\frac{3 12835}{5 \times 5}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3 12835}{5}

r = \pm \frac{3 12835}{5}

Separate the equation into 2 possible cases

r = \frac{3 12835}{5} r = - \frac{3 12835}{5}

Solution

r_{1} = - \frac{3 12835}{5}, r_{2} = \frac{3 12835}{5}

Alternative Form

r_{1} \approx - 67.974995, r_{2} \approx 67.974995

Show Solution